The emails that are 'dropped off' the device as you said, will still be stored on your browser based account. Theyre only removed from the device to keep it tidy and so it doesnt build up a huge backlog of mail =)

As for the browser history, as far as i have found the only history is that saved in the go to window.

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"All of the things I enjoy are immoral, illegal, or fattening" - Oscar Wilde
"All of the things I enjoy have a Wife Approval Factor (WAF) of 0" - Me